Can someone show me how to factor this please?

Answers

Answer 1

Answer:

[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]2\sin ^2 \theta + 3\sin \theta + 1 = 0[/tex]

In the interval [0, 2π).

Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:

[tex]\displaystyle 2u^2 + 3u + 1 = 0[/tex]

Factor:

[tex]\displaystyle (2u+1)(u+1) = 0[/tex]

By the Zero Product Property:

[tex]\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0[/tex]

Solve for each case:

[tex]\displaystyle u = -\frac{1}{2} \text{ or } u = -1[/tex]

Back-substitute:

[tex]\displaystyle \sin \theta = -\frac{1}{2} \text{ or } \sin \theta =-1[/tex]

Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:

[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]


Related Questions

Find the mean, median, and mode of 14, 15, 3, 15, 14, 14, 18, 15, 8, 16.

Answers

Answer:

mean: 13.2 (average)

median: 14.5 (Center)

mode: 14 and 15 (because data is bimodal so there are two modes

Step-by-step explanation:

Answer:

mean = 13.2, median = 15.5, mode = 18

Step-by-step explanation:

mean = 14+15+3+15+14+14+18+15+8+16/10

= 132/10 = 13.2

median =[ (n/2)th term + (n/2+1)term ]/2

here n is even so this formula is applied and before this is done, the numbers given are to be arranged in ascending or descending order

= [10/2 + (10/2+1)]/2

= [5th term + 6th term]/2

= (15+16)/2

= 31/2 = 15.5

mode = 18

what is an expression for...

4x + 4x + 4x + 4x + 4x + 4x

Answers

6(4x) would be the answer

Answer:

24x

Step-by-step explanation:

4x + 4x + 4x + 4x + 4x + 4x

=> 4(x + x + x + x + x + x)

=> 4(6x)

=> 24x

What is 1,025 divided by 68

Answers

Answer:

15.07352941

Step-by-step explanation:

in short 15.07

A simple pulley with the give radius 4 in used to lift heavy objects is positioned 10 feet above ground level. Given that the pully rotates 720 degrees determine the height yo which the object is lifted.

Answers

9514 1404 393

Answer:

  50.3 inches

Step-by-step explanation:

720 degrees is 2 full turns, or twice the circumference of the pulley. The circumference is given by ...

  C = 2πr

  C = 2π(4 in) = 8π in

Then 2 times that is ...

  height lifted = 2(8π in) = 16π in ≈ 50.3 in

The object was lifted about 50.3 inches.

solve for y 7y-3y=8
plzzzz answer
will give brainliest!!!!

Answers

7y - 3y = 8
4y = 8
y = 8/4
y = 2
Hope this helps :)

Answer:

Step-by-step explanation:

7y-3y= 4y

4y=8

Here when its like this we need y by itself, so you take out 4 by dividing 8 by 4.

y= 2

WILL.MARK BRAINLEST. ( The length of a rectangular garden is 5m longer than its breadth .If its perimeter is 150 m,find the area of the garden ) step by step​

Answers

Answer:

1400m^2

Step-by-step explanation:

Solution,

Let the breadth of the rectangle be x m, then the length of the rectangle will be x+5 m,

Now,

Perimeter of the rectangle=2(l+b)

150=2(x+5+x)

150=2(2x+5)

150=4x+10

150-10=4x

140=4x

140/4=x

35=x

So, the breadth of the rectangle=35 m

and length=(35+5)m=40m

Again,

Area of the rectangle=l×b

=40m×35m

=1400 m^2

I hope it helped U

stay safe stay happy

Answer: Area= 1400[tex]meter^{2}[/tex]

Step-by-step explanation:

ok  so  we can assume the

breadth=X

so, length = X+5 (because the length is 5 meters more than the breadth)

perimeter= 150 meters

the formula of the perimeter of a rectangle = 2 x ( Length + Breadth)

so now if we put the values,

2 * ( X+5 +X) = 150 ( because 150 is the perimeter)

2 * (2X + 5) = 150 (the value became 2x because when we add two variables with the same value it will be written as 2(any variable)).

now we multiply  2 with both sides

so ( 2 * 2X) + (2 * 5)

hence, 4X + 10 = 150

now we will solve the equation,

4X= 150 -10 (because we did transposal the signs will change from "+" to "-")

4x= 140

again with the transposal (when we write a number with a variable it shows that it means the number multiplied by the variable in this case it is 4 multiplied by X ) so when we transpose we will have to divide because multiplication turns into division while transposing

so now,

X= 140÷4

which is equal to 35

so finally X = 35

so as we have written in the beginning breadth= X

and LENGTH= X+5

so now we have found X

BREADTH= 35

LENGTH= 40 (because 35+5 is 40)

now we have to find area the formula for finding the area is LENGTH×BREADTH

so, 40 × 35 = 1400

now we put the unit which is square meters also known as [tex]m^{2}[/tex]

so there is your final answer 1400[tex]m^{2}[/tex]

please help me for my homework​

Answers

When converting a decimal to a percent, all you need to do is move the decimal over two places… so, 0.63 becomes 63%
(Basically how 63/100 is the same proportion as 0.63/1.00)

I need help with this problem please explain it good cause I'm rlly confused on how to do like I know how to solve the actual equations like ik how to get -7 and 12 but I don't know how to answer it if that makes sense​

Answers

Answer:

The correct choice is option B. -7 ≤ x < 12

Step-by-step explanation:

(1.2E-3) x (4.6E-1) =

Answers

Answer:

0.0012*​x*​0.46

Step-by-step explanation:

Construct 45° by using set square​

Answers

Place 45

set-square and make an angle of 45

by drawing the rays BD and BC

2. Discounts - You go to the store the next day and the $28.62 shirt is on sale for 15%
off, how much is the shirt before tax?

Answers

Answer:

a = 15 /100  * 28.62 = 4293 /1000

= 4.293

Hope this helps! :)

kiara starts with k marbles iin her collection. she loses 16

Answers

Answer:

Answer: k - 16

Step-by-step explanation:

If she looses, it becomes less or smaller. Subtraction produces that result. K is a fairly large number. 16 is much smaller. So she has K - 16 left.

K - 16

What is the relationship between the number of sides in a regular polygon and
number of lines of symmetry?

Answers

Answer:

Divide 360 by the difference of the angle and 180 degrees. For example, 360 divided by 15 equals 24, which is the number of sides of the polygon. Divide 360 by the amount of the exterior angle to also find the number of sides of the polygon.

1-16 Please helppppp

Answers

Ok fort first second third four ten nine and eight

Drag the numbers below to put them in order from least to greatest:
2.2
2.291 2.27% 2.14 2.26 2.221
Wats the answer?

Answers

2.27% is the least number because since it is a percentage when converted it is 0.0227.
So the answer is :
2.27%, 2.14, 2.2, 2.221, 2.26, 2.291

Show work please

[tex] \sqrt{ \frac{45}{5} } [/tex]

Answers

Answer: 3

Step-by-step explanation:

[tex]\sqrt{ \dfrac{45}{5}} =\sqrt{9}=\bold3[/tex]

Answer:

3

Step-by-step explanation:

We don't really need to simplify this, but if you do:

45/5 is the same as 45 ÷ 5 so

45/5 = 9

Now we have to find the square root of 45/5(or 9). The square root of a number(x for example) is the number(y) that multiplied by itself once will equal x or y · y = x.

For this you can use a calculator:

[tex]\sqrt{\frac{45}{5} }[/tex] = 3

or

[tex]\sqrt{9}[/tex] = 3

Natasha's rectangle measures 4 1/2 units by 2 1/4 units. What is its area?

Answers

Answer:

Answer: 49/6units^{2}49/6units

2

Step-by-step explanation:

You can convert from mixed number to fractions as following:

2 1/3=((2*3)+1)/3=7/3 units

3 1/2=((3*2)+1)/2=7/2 units

Then you can calculate the area of the rectangle as you can see below:

\begin{gathered}Area=lenght*width\\Area=7/2units*7/3units\\Area=49/6units^{2}\end{gathered}

Area=lenght∗width

Area=7/2units∗7/3units

Area=49/6units

2

Answer:

[tex]10\frac{1}{8}[/tex]

Step-by-step explanation:

→ Multiply the fractions together

[tex]4\frac{1}{2} *2\frac{1}{4}[/tex]

→ Convert to improper fractions

[tex]\frac{9}{2} *\frac{9}{4}[/tex]

→ Multiply across

[tex]\frac{81}{8}[/tex]

→ Convert back to mixed number

[tex]10\frac{1}{8}[/tex]

I NEED HELP RN PLEASEE need part 1 and 2 plz asap

Answers

Answer:

A. 2+6+10+14+18+22+26+30+34+38

B. 6+18+54+162+486+1458+4374+13122+39366+118098

Step-by-step explanation:

I. In A. you can see 2 is plus by 4 = 6

                                6 is plus by 4 = 10

                                ... is plus by 4 ...

So the term was plus by 4

II. In B. you can see 6 is multiply by 3 = 18

                                18 is multiply by 3 = 54

                                 ... is multiply by 3 ...

So the term was multiply by 3

Leave comment if you're curious.

find the distance between each pair of points (-1,4) and (1,-1)​

Answers

Answer:

4.5

Step-by-step explanation:

find the difference,square them,add and find the square root

-1-1=-2

4-(-1)=4

2^2+4^2=4+16

=20

square root of 20=4.5(2dp)

23. The table shows the number of hours a group of friends
worked doing various jobs and the amount each earned.
Select the correct hourly rate to complete the table. Then
place a checkmark in the row for the person who had the
greatest hourly rate.
Hours
Amount Earnings Greatest
Worked Earned (s) per hour ($) Hourly Rate?
36.25
Caleb
5
Jeremy
7.5
65.25
Maria
4.25
34.00
Rosa
8
54.00

Answers

calebs hourly rate- $7.25
jeremys hourly rate- $8.70
maria’s hourly rate- $8.00
rosas hourly rate- $6.76

solve the question pls​

Answers

Answer:

[tex]given \: that50 = b \\ a = c \\ 180 - 50 = a = 130 \\ so \: \: \: a = c = 130 \\ b = 50 \\ thank \: you[/tex]

solve for X...........​

Answers

Answer: First Choice. no solution

Step-by-step explanation:

Given

5 (x + 1) ≤ 5x + 3

Expand parentheses and apply the distributive property

5x + 5 ≤ 5x + 3

Subtract 5x on both sides

5x + 5 - 5x ≤ 5x + 3 - 5x

5 ≤ 3

5 ≤ 3 is not true, therefore, there is no solution.

Hope this helps!! :)

Please let me know if you have any questions

f(x) = (x + 1)(x - 5). What is the vertex?
(1,5)
(5.1)
(2.-9)
(-9,2)​

Answers

Answer:

(2, -9)

Step-by-step explanation:

f(x) = (x + 1)(x - 5)

[tex] =f(x) = {x}^{2} - 5x + x - 5[/tex]

[tex] = f(x) = {x}^{2} - 4x - 5[/tex]

[tex] = f(x) = {1x}^{2} - 4x - 5[/tex]

[tex] = f(x) = {1x}^{2} + ( - 4x) - 5[/tex]

= a = 1, b = -4

[tex] = x = \frac{ - 4}{2 \times 1} [/tex]

[tex] = x = - \frac{ - 4}{2} [/tex]

[tex] = x - ( - 2)[/tex]

[tex] = x = 2[/tex]

= f(x) = (x + 1) x (x - 5); x = 2

= f(2) = -9

= (2, -9)

What is 50x30 I really need to know

Answers

Answer:

1500

Step-by-step explanation:

Basically 5*3 then add the two zeroes. One from 50 and 30.

the answer is 1500 if you do 5x3= 15 and there’s two zeros in the problem so you add that and it’s 1500


Hello!
Im beginning year 11 this year and I recently did really bad in my Mocks! I really need some help and advice for all of my subjects because I truly dont know how to revise effectively and because I keep Procrastinating!
Any advice would be appreciated or if u have links to videos and helpful websites I would appreciate it
Here are my results :
Maths : 4
Eng Language : 4
Eng Lit : 4
Chemistry : 4
Physics : 3
Biology : 3
RE: 4
Health and Social care : Level 2 Pass
History : 4
Food Tech : 4
Spanish : 4
Thank u!

Answers

Answer:

if you need help with some subjects you can come here in brainly it helps me a lot i just started grad 6 so yeah

like if you have a math question just go to ask question you and someone will help

and also explain so yeah  hope i helped a little

ABCD is rotated counterclockwise about the origin. By how many degrees
was ABCD rotated?
O A. 360°
• B. 180°
• C. 270°
O D. 90°

Answers

Answer:

B. 180 degrees

Step-by-step explanation:

They are exactly across from one another. Here, this will make more sense.

               0 (starting point)

               |

 270--            -- 90

               |

             180 (where you ended up)

Now till the screen towards the right. The zero and the 180 should be pointing in the same direction as the squares.

Degrees was ABCD rotated or transformed  to form A'B'C'D' is  180 degrees about the origin .

What is rotation in graph?

In geometry, a transformation  is an operation that moves, flips, or changes a shape to create a new shape. A rotation is an example of a transformation where a figure is rotated about a specific point (called the center of rotation), a certain number of degrees.

According to the question

ABCD is rotated counterclockwise about the origin.  

Degrees was ABCD transformed to form A'B'C'D' is

180 degrees about the origin

As when we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.

So, as per figure ABCD which is in first quadrant were x and y both are positive and  figure A'B'C'D' third quadrant were x and y both are negative.

Hence, Degrees was ABCD rotated or transformed  to form A'B'C'D' is  180 degrees about the origin .

To know more about rotation in graph here:

https://brainly.com/question/12091224

#SPJ2

5x + 2) mize
2.
P has coordinates (2, 4). Q has coordinates (-10, 12). Find the midpoint of PQ.
122

Answers

I believe the midpoint should be (-4, 8)

Martin spent $300 from his savings account on a new bike. He also deposited $300 in his savings account that he earned from selling his used textbooks. Which integer represents the change in Martin's savings? A) $100 B $0
C. -100$ D. -$200​

Answers

Answer:

B

Step-by-step explanation:

a money account works in the same way as real things we can touch.

so, when I have 300 apples at a place (e.g. a grocery store), then I take away 300 apples, and then put again 300 apples there - how many apples will be there at that moment ?

we had 300 and took away 300.

300 - 300 = 0

at that moment we have 0 apples.

but then we put again 300 apples there.

0 + 300 = 300

so, we end up with 300 apples. the same number we started with.

and the same way for the savings account.

he takes out $300.

that means he has now $300 less on his account.

and then he adds $300.

so, he added exactly the same amount as he took out earlier, which means nothing else than that he undid his earlier action regarding his bank account.

so, his balance is now exactly the same as before he did the first transaction.

therefore the change is exactly : $0

If a1=1. And r=1/5 find a8

Answers

Answer:

a₈ = [tex]\frac{1}{78125}[/tex]

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

Here a₁ = 1 and r = [tex]\frac{1}{5}[/tex] , then

a₈ = 1 × [tex](\frac{1}{5}) ^{7}[/tex] = 1 × [tex]\frac{1}{78125}[/tex] = [tex]\frac{1}{78125}[/tex]

Which of the following numbers is irrational?
OA) -7.8 repeating
OB) 25
OC) 25.8125
OD 0.025

Answers

-7.8

The rest can be solved as rational. Negative numbers are not rational.

Answer:

OA) -7.8 repeating... is irrational number

Step-by-step explanation:

I. Repeating Decimal is on of irrational number

II. Pie.value is also irrational number, but in computer science, we can find pie value with the quantum computer.

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